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Practice: Adjoint Matrix

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Wize University Linear Algebra Textbook > Matrices

Matrix Inverse Algorithm

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Let B=[1−102111000−11−21−2−1]B=\left[\begin{array}{rrrr} 1&-1&0&2\\ 1&1&1&0\\ 0&0&-1&1\\ -2&1&-2&-1 \end{array}\right], and note that det(B)=−1\text{det}(B)=-1

Use the determinant and the adjoint of BB to find the entry in position (4,3)(4,3) of the matrix B−1B^{-1}
More Matrix Inverse Algorithm Questions:
Practice: Method of Inverse
Practice Question: Method of Inverse
Given the matrix A=[2130101−12]A=\left[\begin{array}{rrr} 2&1&3\\ 0&1&0\\ 1&-1&2 \end{array}\right],
Practice: Method of Inverse
Practice Question: Method of Inverse
Given the matrix A=[2130101−12]A=\left[\begin{array}{rrr} 2&1&3\\ 0&1&0\\ 1&-1&2 \end{array}\right],
Practice: Matrix Inverse
Practice Question: Matrix Inverse
For what value(s) of k will the matrix[1210150k1]\begin{bmatrix} 1&2&1\\ 0&1&5\\ 0&k&1 \end{bmatrix} be invertible?
Practice: Matrix Inverse
Practice Question: Matrix Inverse
For what value(s) of k will the matrix[1210150k1]\begin{bmatrix} 1&2&1\\ 0&1&5\\ 0&k&1 \end{bmatrix} be invertible?
Practice: Matrix Inverse
Practice Question: Matrix Inverse
For what value(s) of k will the matrix[1210150k1]\begin{bmatrix} 1&2&1\\ 0&1&5\\ 0&k&1 \end{bmatrix} be invertible?
Practice: Matrix Inverse
Practice Question: Matrix Inverse
For what value(s) of k will the matrix[1210150k1]\begin{bmatrix} 1&2&1\\ 0&1&5\\ 0&k&1 \end{bmatrix} be invertible?
Practice: Matrix Inverse
Practice Question: Matrix Inverse
For what value(s) of k will the matrix[1210150k1]\begin{bmatrix} 1&2&1\\ 0&1&5\\ 0&k&1 \end{bmatrix} be invertible?
Practice: Matrix Inverse
Practice Question: Matrix Inverse
For what value(s) of k will the matrix[1210150k1]\begin{bmatrix} 1&2&1\\ 0&1&5\\ 0&k&1 \end{bmatrix} be invertible?
133 - FML 3 - 18.1W e.g. 10
Find the value(s) of c such that A is NOT invertible given A=  [c−c1−1−1−11−cc]\bcb{\boldsymbol{ A =  \begin{bmatrix} c & -c & 1 \\ -1 & -1 & -1 \\ 1 & -c & c \end{bmatrix} }}
Practice: Matrix Inverse
Find all values of k so that the matrix [−2003102−1k]\begin{bmatrix} -2&0&0\\ 3&1&0\\ 2&-1&k \end{bmatrix} has an inverse.
Find the inverse of A=[101011110]A=\begin{bmatrix} 1&0&1\\ 0&1&1\\1&1&0 \end{bmatrix} .
For each of the following matrices, find the inverse or state why the inverse does not exist.
A=[1−1−2100012]A=\begin{bmatrix} 1&-1&-2\\ 1&0&0\\ 0&1&2 \end{bmatrix}
B=[3191506]B=\begin{bmatrix} 3&1&9\\ 15&0&6 \end{bmatrix}
Practice: Matrix Inverse
Find all values of k for which the matrix [2−6−1k2−22]\begin{bmatrix} 2&-6\\ -1&k^2-22 \end{bmatrix} has no inverse.
Practice: Matrix Inverse
Find the inverse of the following matrices:
a.) A=[4534]A=\begin{bmatrix} 4&5\\ 3&4 \end{bmatrix}
b.) B=[−1−2024113−2]B=\begin{bmatrix} -1&-2&0\\ 2&4&1\\ 1&3&-2 \end{bmatrix}
Matrix Inverse
Practice: Matrix Inverse
If [1ax2by0cz]\left[\begin{array}{c} 1&a&x\\ 2&b&y\\ 0&c&z \end{array}\right] is the inverse of the matrix[1p0−3q42r1]\left[\begin{array}{c} 1&p&0\\ -3&q&4\\ 2&r&1 \end{array}\right], find the value of rr.
Let A=[214103421]A=\begin{bmatrix}2&1&4\\1&0&3\\4&2&1\end{bmatrix}. Find A−1A^{-1} if possible.
Find the inverse of [021255121]\begin{bmatrix} 0 &2& 1\\ 2 &5 &5\\ 1 &2 &1 \end{bmatrix}
The following matrix A depends on a parameter p. Find all the values of the parameter p for which the
corresponding matrix is not invertible.
A=[123410002000300040010𝑝𝑝+1𝑝+20−𝑝−2𝑝+1−3𝑝+2]A=\begin{bmatrix} 1&2&3&4\\ 1000&2000&3000&4001\\ 0&𝑝&𝑝 + 1&𝑝 + 2\\ 0&−𝑝&−2𝑝 + 1&−3𝑝 + 2 \end{bmatrix}
For what value or values of a (if any) is the matrix below invertible?
[1210350𝑎1]\begin{bmatrix} 1& 2& 1\\ 0 &3& 5\\ 0 &𝑎 &1 \end{bmatrix}
The following matrix A depends on a parameter p. Find all the values of the parameter
p for which the corresponding matrix is not invertible.
A=[123410002000300040010𝑝𝑝+1𝑝+20−𝑝−2𝑝+1−3𝑝+2]A=\begin{bmatrix} 1&2&3&4\\ 1000&2000&3000&4001\\ 0&𝑝&𝑝 + 1&𝑝 + 2\\ 0&−𝑝&−2𝑝 + 1&−3𝑝 + 2 \end{bmatrix}
Practice Question 3: Matrix Inverse
Practice Question: Matrix Inverse
For what value(s) of k will the matrix[1210150k1]\begin{bmatrix} 1&2&1\\ 0&1&5\\ 0&k&1 \end{bmatrix} be invertible?
Find all the values of k for which the matrix A has an inverse
A=[210102102k]A=\begin{bmatrix} 2&1&0\\ 1&0&2\\ 1&0&2k \end{bmatrix}
Practice: Method of Inverse
Practice Question: Method of Inverse
Given the matrix A=[2130101−12]A=\left[\begin{array}{rrr} 2&1&3\\ 0&1&0\\ 1&-1&2 \end{array}\right],
Find all the values of 𝑘 such that the matrix 𝐴=[33−610−k2]has an inverse.\text{Find all the values of 𝑘 such that the matrix 𝐴}=\begin{bmatrix} 3&3\\ -6&10-k^2 \end{bmatrix}\text{has an inverse.}
Matrix Inverse
If [1ax2by0cz]\left[\begin{array}{c} 1&a&x\\ 2&b&y\\ 0&c&z \end{array}\right] is the inverse of the matrix[1p0−3q42r1]\left[\begin{array}{c} 1&p&0\\ -3&q&4\\ 2&r&1 \end{array}\right], find the value of rr.
Find the inverse of the matrix [10221−13−215]\begin{bmatrix} 1&0&2\\ 2&1&-1\\ 3&-2&15 \end{bmatrix}.
Matrix Inversion Algorithm
Example: Matrix Inverse Algorithm
Find the inverse of A=[1325]A=\left[\begin{array}{rr}1 & 3\\2 & 5\end{array}\right] using the formula for a 2×22\times2 matrix, and using the Gauss-Jordan elimination algorithm.
Find the inverse of the matrix A=[10221−13−215]A=\left[\begin{array}{rrr} 1&0&2\\ 2&1&-1\\ 3&-2&15 \end{array}\right]
Matrix operations
Suppose that A=[1−103−20041]A=\begin{bmatrix}1 & -1 & 0\\3 & -2 & 0\\0 & 4 & 1\end{bmatrix}and BBis a 3×23 \times 2matrix. If the product AB=[34011−2]AB = \begin{bmatrix}3 & 4\\0 & 1\\1 & -2\end{bmatrix}, find the (1,2)-entry of BB(i.e. B12B_{12}).
Invertible matrix
For what value(s) of aawill the matrix [2−43a]\begin{bmatrix}2 & -4\\3 & a\end{bmatrix} be invertible?
Matrix Inverse
Practice: Matrix Inverse
If [1ax2by0cz]\left[\begin{array}{c} 1&a&x\\ 2&b&y\\ 0&c&z \end{array}\right] is the inverse of the matrix[1p0−3q42r1]\left[\begin{array}{c} 1&p&0\\ -3&q&4\\ 2&r&1 \end{array}\right], find the value of rr.
Practice Question: Matrix Inverse
Practice Question: Matrix Inverse
If [1ax2by0cz]\left[\begin{array}{} 1&a&x\\ 2&b&y\\ 0&c&z \end{array}\right] is the inverse of the matrix[1p0−3q42r1]\left[\begin{array}{} 1&p&0\\ -3&q&4\\ 2&r&1 \end{array}\right], find the value of rr.
Suppose that A=[1−1031−4]A=\begin{bmatrix}1 &-1&0\\3&1&-4\end{bmatrix} and RRis the reduced row echelon form of AA. Find the invertible matrix UUsuch that R=UAR=UA.
For what value(s) of aawill the matrix [2−43a]\begin{bmatrix}2 & -4\\3 & a\end{bmatrix}be invertible?
Practice: Matrix Inverse
Find all values of k for which the matrix [2−6−1k2−22]\begin{bmatrix} 2&-6\\ -1&k^2-22 \end{bmatrix} has no inverse.
Practice: Matrix Inverse
Practice Question: Matrix Inverse
Find all the values of kk such that the matrix[210102102k]\begin{bmatrix} 2&1&0\\ 1&0&2\\ 1&0&2k \end{bmatrix} has an inverse.
Practice: Matrix Inverse
Practice Question: Matrix Inverse
For what value(s) of k will the matrix[1210150k1]\begin{bmatrix} 1&2&1\\ 0&1&5\\ 0&k&1 \end{bmatrix} be invertible?
Practice: Matrix Inverse
Practice Question: Matrix Inverse
For what value(s) of kk will the matrix[1210150k1]\left[\begin{array}{rrr} 1&2&1\\ 0&1&5\\ 0&k&1 \end{array}\right] be invertible?
Practice Question 1: Matrix Inverse
Practice Question: Matrix Inverse
Find all the values of kk such that the matrix[210102102k]\begin{bmatrix} 2&1&0\\ 1&0&2\\ 1&0&2k \end{bmatrix} has an inverse.
Practice: Matrix Inverse
Find all values of k so that the matrix [−2003102−1k]\begin{bmatrix} -2&0&0\\ 3&1&0\\ 2&-1&k \end{bmatrix} has an inverse.
Practice: Matrix Inverse (~2016 Test2 #15)
Practice: Matrix Inverse
Find all the values of kk such that the matrix[210102102k]\begin{bmatrix} 2&1&0\\ 1&0&2\\ 1&0&2k \end{bmatrix} has an inverse.